NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 46 - 53 of 231
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Question 46
Appeared in Year: 2010
Describe in Detail Subjective▾
Let C be the semicircle where varies from , in the complex plane. Evaluate:
EditExplanation
Equation of given circle is
… (63 more equations) …
Question 47
Appeared in Year: 2009
Write in Short Short Answer▾
Let
Write down the residues of at each of its poles
EditQuestion 48
Appeared in Year: 2007
Describe in Detail Subjective▾
Let C denote the Boundary of the square whose sides are given by the lines . Assume that C is described in the position sense, i.e.. anticlockwise. Evaluate
EditExplanation
To evaluate
Take
H…
… (94 more equations, 12 figures) …
Question 49
Explanation
Now
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Question 50
Appeared in Year: 2009
Describe in Detail Subjective▾
Let C be the contour consisting of the lines , described counterclockwise in the plane. Compute
EditExplanation
is the contour shown in the figure
To evaluate
… (72 more equations, 9 figures) …
Question 51
Appeared in Year: 2017
Describe in Detail Subjective▾
Let Write down the Taylor Expansion of f in the neighbourhood of .
EditExplanation
Here
Put
… (68 more equations) …
Question 52
Appeared in Year: 2015
Describe in Detail Subjective▾
In each of the following cases, state whether the given series is absolutely convergent, conditionally convergent or divergent
a)
b)
c)
EditExplanation
Option (a) The given series is
Where
… (939 more equations) …
Question 53
Appeared in Year: 2006
Question MCQ▾
Pick out series which are absolutely convergent.
Choices
Choice (4) | Response | |
---|---|---|
a. | ||
b. | ||
c. | ||
d. | Both a. and b. are correct |